The measurement of partial pressures and concentrations of oxygen is of great importance in many areas of biology, medicine, (bio)chemistry, (bio)physics and engineering. This measurement can be accomplished with various degrees of accuracy and resolution using a wide variety of instrumentation and methodology, from simple manometric and chemical assays to high resolution gas chromatography, neutron activation and positron emission tomography. Techniques used to measure oxygen content in solids (which will not be discussed) differ substantially from those used to measure oxygen content in liquids and gases, and for the last two phases, the techniques can vary substantially depending on the physical and chemical environment of the sample.
For temperatures in the biological range (e.g. 0.degree.-50.degree. C.) it is often necessary to measure and/or control oxygen concentrations both in the gas and the liquid phase and this type of measurement can only be made with a membrane covered polarographic sensor of the type disclosed in U.S. Pat. No. 2,913,386, issued Nov. 17, 1959 to Leland C. Clark, Jr., and hereinafter referred to as a "Clark" sensor. In this type of sensor, oxygen is reduced by a noble metal cathode, whose potential is fixed with respect to a reference anode (often Ag-AgCl), both elements of the cell in an aqueous electrolyte and enclosed by a gas-permeable membrane. Unfortunately, many scientific studies involve reactions which are modulated by very small concentrations of oxygen and both the resolution and the response time of typical Clark sensors are often inadequate in monitoring such reactions (C. J. Koch, Oxygen Effects in Radiobiology. In: Hyperthermia (Hl Bicher & DF Bruley, eds) Adv. Exp. Med. & Biol., Vol. 157, 123-144, Plenum Press, New York, 1983).
One can easily list several criteria of importance in determining the overall quality of a sensor. Some of the criteria are quantitative in that absolute numbers can be assigned to them:
1a) Sensitivity: the magnitude of the response produced by a given partial pressure of oxygen (e.g. 0.5 nanoamps [nA] per kilopascal [kPa] of oxygen partial pressure [pO.sub.2 ]). The current generated by the sensor will be directly related to the amount of oxygen consumed by the sensor--see 8a below for importance--and below a certain value, the current becomes increasingly difficult to measure accurately (state-of-art circuitry allows the measurement of currents below 1 picoamp only with great difficulty and cost).
2a) Minimum Value of "Zero" Current: the equilibrium value of response as a function of some reference value for a sensor in an environment of zero oxygen (e.g. 0.1% of response in air).
3a) Stability of "Zero" Current: the change in response of a sensor in an environment of zero oxygen per unit time (can include linear, exponential and random components).
4a) Noise: the random fluctuations in response of a sensor in high or low concentrations of oxygen (e.g. of air value or % of scale).
5a) Stability: the relative change in response (i.e. current) of a sensor per unit time in a constant environment (pO.sub.2, ionic strength, temperature) (e.g.-0.5%/hr).
6a) Linearity: the range of oxygen partial pressures over which the relationship between oxygen partial pressure and sensor response is linear to some specified accuracy (it is common for sensors to deviate from linearity at very high and at very low partial pressures of oxygen).
7a) Response Time: the time for a given percentage change in response after a step change in oxygen partial pressure in the external environment of the sensor (usually 1/e of step value). An ideal sensor would approach the new value exponentially with a single time constant but most sensors have two or more associated time constants, the relative importance of which depends upon the absolute values of oxygen partial pressure before and after the step change. Usually the most stringent test involves a step change in oxygen partial pressure from a high value (i.e. ambient air) to zero.
8a) Stirring Requirements in Liquids: the required velocity of the liquid of interest to minimize the response differential of the sensor between gas and gas-equilibrated liquid. This parameter should be expressed both as liquid-sensor velocity to achieve a given percentage of the gas phase response, and as maximum percentage decrease when the sensor is added to an unstirred solution which was in equilibrium with the gas phase.
Other aspects of sensor design can be just as important for practical usage but are inherently qualitative in nature.
9a) Shieldinq Efficiency: the relative isolation of the performance of a sensor and its associated electronic amplifier in the environment of other laboratory equipment and large moving charged bodies (people).
10a) Structure: the aspects of shape, size and materials of sensor construction which may enhance or limit its range of applications. For example, there would be no point in having a sensor which could measure oxygen accurately at low levels but which could not be sealed into a closed volume without leakage or presence of air bubbles etc. It is equally important that the sensor body have a stable shape (e.g. plastics swell in water) and that this shape be suitable for fitting into a variety of standard vessels (e.g. many commercial sensors have their active tip as the widest part of the sensor, making it impossible to insert into standard fittings without disconnecting the sensor or having to reapply the membrane). An often overlooked factor is the contamination of the bulk of the sensor by oxygen and other chemicals from previous environments and conversely the contamination of samples by materials from the bulk of the sensor. For example if one is attempting to monitor an oxygen dependent reaction in a small closed volume, the plastic body of a sensor can give off large quantities of dissolved oxygen.
11a) Consistency of Response to Changes in Environment: the consistency of sensor response to changes in sensor environment such as pressure (i.e. one would hope to obtain the same response with 1% oxygen plus 99% nitrogen at 101 kPa pressure, as with 100% oxygen at 1.01 kPa pressure). In addition, the temperature dependence of the sensor should be reproducible and without hysteresis. Often one is required to monitor oxygen concentrations in an extremely humid environment and this poses rather severe problems for the electrical connections to the sensor, because large leakage currents can result from damp connections and cable.
12a) Electronic Amplification Requirements (see also 5a): the current gain necessary to accurately convert the oxygen-derived sensor current to a form suitable for monitoring purposes--usually a full scale output of the order of 1 volt. Sensors available at the present time have a very broad range of sensitivities (10.sup.-10 -10.sup.-7 A/kPa pO.sub.2). One usually obtains the highest sensitivities at the expense of some other quality factors. Since many experiments require measurements of the order of 0.01 kPa of oxygen partial pressure, the resolution of the amplification system must be at least as sensitive as 10.sup.-12 A and preferably even better for the less sensitive devices. Thus, the development of significantly better sensors requires state-of-the-art electronic measurement techniques.
13a) Interference: the response of the sensor to any other than the desired molecule which can diffuse through the membrane and react with the redox-processes ongoing. Several gases have been reported to do so with polarographic oxygen sensors (CO.sub.2, N.sub.2 O, H.sub.2 S, SO.sub.2, NO, NO.sub.2) but it may be possible to reduce such interference by proper mechanical and electro-chemical design.
Commercial prior art polarographic oxygen sensors include those manufactured by Beckman Instruments (Model 325814 - no longer available, and patented under aforesaid U.S. Pat. No. 2,913,386, issued Nov. 17, 1959 to Leland C. Clark, Jr.), Yellow Springs Instruments (Model 5331, disclosed in U.S. Pat. No. 3,406,109 issued Oct. 15, 1968 to Everett W. Malloy), and Diamond Electrotech (formerly Transidyne General Corporation-Model 730).
One can much more easily appreciate the concepts of response time, zero current and noise by measuring as a function of time the response of an oxygen sensor after its environment is rapidly changed from a high oxygen partial pressure (i.e. air) to zero. Such measurements, using the best responders of several each of the sensors described above, have shown an initial rapid decrease in current to 2-10% of that in air, but then a much slower decrease, taking many hours, to a minimum value of 0.2-2% of that in air. Some of the poorer responders had zero currents several fold higher and more in keeping with their actual specifications. Others had zero currents which remained large and variable.
Furthermore, it was found that the magnitude of the zero current was not independent of the previous environment of the sensor (C. J. Koch and J. Kruuv, Measurement of very low oxygen tensions in unstirred liquids. Analyt. Chem. 44 1258-1263, 1972), and this probably points to one source of the zero current, namely dissolved oxygen in the body, typically plastic, of the sensor itself. Under some circumstances one can measure small quantities of oxygen in the presence of a large zero current if one is able to continually switch back and forth between the gas to be monitored and a true "zero oxygen" gas but this is seldom possible. Such switches for measurements in liquids are virtually impossible.
The highly variable nature of the zero current and the other response parameters led the present inventor to believe that flaws in available sensors were expressing themselves to varying degrees, and that perhaps a much improved sensor would be possible if these flaws could be identified and corrected. Unfortunately, the flaws have been "over" identified in the literature, since changing almost any aspect of the operation of a sensor changes its response to some degree. Therefore, the approach taken was to re-examine the basic aspects of design and operation of polarographic sensors, to see if flaws could be predicted in their performance and to devise construction methods to correct or minimize these flaws.
The electrochemical processes have not been described quantitatively but there is certainly general agreement about the basic anode and cathode reactions (see Irving Fatt: "Polarographic Oxygen Sensors", CRC Press, Cleveland 1976; D. J. G. Ives and G. J. Janz: "Reference Electrodes", Academic Press, New York, 1961). EQU At Cathode: O.sub.2 +4e.sup.- +4H.sup.+ .fwdarw.2H.sub.2 O [r1]
Note that H.sup.+ and other cations present in the electrolyte will be attracted to the cathode so that the "pH" near the oxygen reductive surface will be more acidic than the "pH" of the electrolyte as mixed in bulk solution. EQU At Anode: 4Ag+4Cl.sup.- .fwdarw.4AgCl+4e.sup.- [r 2]
The converse will be true for the anode (i.e. OH.sup.- and anions attracted) but the surface area of the anode is usually so much larger than that of the cathode, that pH changes would only be expected to affect the cathode reactions.
Although reactions r1 and r2 are often given in descriptions of polarographic sensors, there is not much evidence that they actually occur in this manner. For example, it is clear that almost all non-enzyme mediated (and probably most enzyme-mediated) redox reactions occur in 1 electron steps. This means that the 4 electron reduction would have to proceed through O.sub.2.sup.-. or HO.sub.2., H.sub.2 O.sub.2 and OH.: EQU O.sub.2 +e.sup.- +H.sup.+ .fwdarw.O.sub.2.sup.-. +H.sup.+ .rarw.pKa=4.3.fwdarw.HO.sub.2.sup.. [r3] EQU O.sub.2.sup.-. +e.sup.- +2H.sup.+ .fwdarw.H.sub.2 O.sub.2 [r 4]
or EQU 2O.sub.2.sup.-. +2H.sup.+ .fwdarw.H.sub.2 O.sub.2 +O.sub.2 [r 4b]
or EQU HO.sub.2.sup.. +e.sup.- +H.sup.+ .fwdarw.H.sub.2 O.sub.2 [r 4c]
or EQU O.sub.2.sup.-.+HO.sub.2.+H+.fwdarw.O.sub.2 +H.sub.2 O.sub.2[r 4d] EQU H.sub.2 O.sub.2 +e.sup.- .fwdarw.OH.sup.- +OH.sup.. [r5] EQU OH.+e-.fwdarw.OH- [r6]
Reactions r4a and r4b are likely to be extremely slow. Even reaction r5 is much slower than reaction r3. In fact, at relatively low polarizing voltages (e.g. 0.55 volt) the response of a typical oxygen sensor (without its membrane) in a deoxygenated hydrogen peroxide solution is less than 1/10th that in a solution with the same concentration of oxygen (unpublished observation). From inspecting these reactions, and noting that the electrolyte tends to become more basic, one might expect that the optimal pH for sensor operation might fall within the acid range. This is because the very slow reactions (r4a and r4b) must predominate at neutral and higher pH's. However, in agreement with other investigators this inventor has found the most reproducible responses under basic conditions. Similarly, in agreement with Hahn et al. ( C. E. W. Hahn, A. W. Davis & W. J. Albery, Electrochemical Improvement in the Performance of pO.sub.2 Electrodes, Resp. Physiol. 25, 109-133, 1975) this inventor has sometimes found an improved and more stable zero current when a trace of catalase is added to the electrolyte. With the sensors according to the present invention, which already have a much reduced zero current, the presence of catalase can cause negative currents in the absence of oxygen. This may be due to a preferential build-up of superoxide which may actually be oxidized rather than reduced in the absence of oxygen. The point of this discussion though is that an "improved" response of a particular sensor under certain specified conditions may result from more than one interacting phenomena. Thus, the improvement may not be found under other circumstances and its cause may not be fully understood.
The linearity of a Clark sensor depends on the condition that the reduction of oxygen and its reduced products (reactions r3 to r6) at the cathode maintains their concentration in the immediate vicinity of the cathode at essentially zero. Thus, since the oxygen gradient across the membrane will be linear (there is no oxygen consumption within the membrane), the flux of oxygen through the membrane will simply be proportional to the oxygen partial pressure in the environment external to the membrane (external environment). The proportionality constant must allow for the very different solubility and diffusion constants of the external environment, the membrane and the electrolyte. The flux of oxygen from the external environment can cause a decrease in partial pressure at the interface of membrane and external environment if the diffusion constant of the external environment is small enough and/or the flux is large enough. Thus in order to minimize the difference in sensor response between gas and gas-equilibrated liquid, it is desirable to decrease this flux by increasing the relative diffusion barrier of the membrane (i.e. thicker membrane or smaller diffusion constant) and/or decreasing the size of the cathode. There is a tradeoff involved however because these measures have the effect of reducing the sensitivity.